A piece of string is $ 30 \mathrm{~cm} $ long. What will be the length of each side if the string is used to form:
(a) a square?
(b) an equilateral triangle?
(c) a regular hexagon?

Given:

A piece of string is 30 cm long.

To do:

We have to find the length of each side when the string is used to form:

(a) a square

(b) an equilateral triangle

(c) a regular hexagon

Solution:

The perimeter of each of the forms is equal to the length of the string in each case.

Therefore,

(a) The perimeter of the square form of the string $ =30\ cm$

We know that,

The perimeter of a square is four times its side.

$4\times$ each side of the square $ =30\ cm$

Each side of the square $=\frac{30}{4}$

$ =7.5\ cm$

The length of each side of the square is $7.5\ cm$

(b) The perimeter of the equilateral triangle form of the string $ =30\ cm$

We know that, 

The perimeter of an equilateral triangle is three times its side

$3\times$ each side of the triangle $ =30\ cm$

Each side of the triangle $ =\frac{30}{3}$

$ =10\ cm$

The length of each side of the triangle is $10\ cm$.

(c) The perimeter of the regular hexagon form of the string $ =30\ cm$

We know that, 

The perimeter of a regular hexagon is six times its side

$6\times$ each side of the regular hexagon $ =30\ cm$

Each side of the regular hexagon $ =\frac{30\ cm}{6}$

$ =5\ cm$

The length of each side of the regular hexagon is $5\ cm$.